It is desirable to solve Maxwell's equations for various electric and magnetic media using the finite-difference time-domain (FDTD) method to simulate electromagnetic properties of the media. The FDTD method involves spatially discretizing the volume of the medium being simulated to form a mesh of individual elements. The individual elements can be referred to as mesh cells or Yee cells. The FDTD method is routinely used to simulate isotropic materials.
It can also be desirable to also solve equations involving anisotropic media to model the electrical and magnetic properties of media in various systems and devices. For example, it may be desirable to simulate the electromagnetic properties of liquid crystals in the conception, design, and testing of liquid crystal displays (LCDs) and electrical drivers. However, anisotropy complicates the solution of Maxwell's equations using the FDTD method.
Solving Maxwell's equations in anisotropic materials enables the simulation of electromagnetic properties of device designs comprising such materials. However, simulation of anisotropic materials can be complicated by spatially varying permittivity. For example, liquid crystal modeling can be challenging in cases where the orientation of liquid crystal molecules is a function of three-dimensional space.
The simulation of electromagnetic properties is also complicated in cases where at least some of the terms in the permittivity tensor are dispersive. These terms may be approximated by FDTD models including Plasma-Drude, Lorentz, Debye and more general multi-pole expansion dispersive models.
Although attempts have been made to overcome the above deficiencies, these have focused on sub-element smoothing or conformal mesh algorithms to reduce the number of errors that occur at interfaces between different media on the finite sized mesh used in the simulation. Solving Maxwell's equations in the simulation of electromagnetic properties of general dispersive, anisotropic, spatially varying media remains difficult due to challenges in computing numerical solutions to Maxwell's equations.
It is an object of the present invention to mitigate or obviate at least one of the above disadvantages.